Why activated sludge method needs reflux sludge, how to determine the reflux ratio

Activated sludge method relies on the removal of BOD by biological sludge, the biomass of influent water is limited, so it should be separated from the secondary sedimentation tank sludge reflux, part of the aeration tank. The size of the reflux ratio depends on the concentration of sludge in the aeration tank X and the concentration of reflux sludge Xr, according to the balance of sludge in and out of the aeration tank r = (Xr-X)/X